(a) A rectangular block has the dimensions l w h . When a battery with a voltage

Question

                    (a) A rectangular block has the dimensions l w h. When a battery with a voltage V is connected across the end faces as shown in                     the left figure, a current I1 flows through the circuit. If the same battery is connected across the top and bottom                     faces of the block as shown in the right figure, what is the current I2 that flows through the circuit? Give your                     answer in terms of I1. (Use the following as necessary: , w, h, I1)                 

                    I2 =____?                 

                    (b) Suppose = 4.60 cm, w = 2.2 cm, and h = 1.00 cm; the battery voltage is 1.5 V and                     I1 = 2.90 A, determine the value of I2.                 

                    _______A                 

Explanation / Answer

1.) V = I1*R1

R1 = ro*l/A

A = wh

R1 = ro*l/wh

from this

ro = Vwh/I1L

Now,

V = I2R2 = I2*ro*h/(wL) = I2*(Vwh/I1L)*(h/wL) = I2*(V/I1)*(h/L)^2

I2 = I1*(L/h)^2

2.) I2 = 2.9*(4.6/1)^2 = 61.3A

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